A Note on Minimal Models(Mathematical Logic and Applications'92)
Koichiro Ikeda · Institutional Repositories DataBase (IRDB) · 1993
A model $M$ is said to be minimal if there is no proper elementary submodel of $M$ .We consider the size of an indiscernible set in a minimal model.$h[2]$ Shelah showed that if a theory $T$ is $\omega$ -stable then there is no infinite indiscernible set in a minimal model of $T$ .On the other hand Marcus [1] constructed a theory having a minimal (and prime) model with an infinite indiscernible set.The theory is stable but non-superstable.In this note we show the following theorem: THEOREM.Let $T$ be superstable and let $A$ be any set.Then there is no minimal model over A which has an infinite set of indiscernibles over $A$ .